Hi Fan, very insightful! Thank you.

Hi Zheng,

Thanks for your comment and good questions!

1) The instability pattern in Fig. 3a actually shows a mixed mode in the rolling up of the sleeve, where you would see wrinkles, ridges, sagging ridges and even diamond-like shape all together. This is mainly attributed to the random imperfections (non-uniform radius of arm and material of sleeve), perturbations (load and stimuli) and considerbale gaps between the sleeve and the arm in such rough test. Imperfections and perturbations can trigger multiple ridges where such 'defects' are located, while the gap between the sleeve and the arm leads to a diamond-like mode, consistent with the early experiments in 1960s where an internal solid mandrel was introduced to artificially stabilize deflections in the shell and all those experiments revealed non-axisymmetric diamond-like patterns (see more discussion in supplementary of our paper). In the ideal situation, the nonlinear postbuckling behavior involving succesive bifurcations (note that wrinkle-to-ridge and ridge-to-sagging are subcritical and thus imperfection-sensitive, see Maxwell energy in our paper) physically exists in the bifurcation diagram (Fig. 3), where the amplitude of ridge is in the order of ~sqrt(Rh), while the maximum amplitude of wrinkles is nearly half ~0.4*sqrt(Rh). All in all, we thus more often observe such mixed instaiblity pattern (Fig. 3a) upon rolling up our sleeves.

2) The experiment was based on wet surface chemical oxidation of aqueous-phase-synthesized polydimethylsiloxane (PDMS) microspheres in the mixed H2SO4/HNO3/H2O solution (more details can be found in the paper). In fact, it is really a challenge to measure whether and how the surface energy works in situ, yet the final wrinkling modes suggest that the pattern selection can be primarily determined by a single parameter Cs which characterizes the macroscopic stiffness ratio of core/shell and geometric curvature of the system.

Hi Fan,

Thanks for your post, very informative and inspiring! I have two quick questions:

1) I am fascinated with your work on smooth-wrinkle-ridge-sagging transitions in compressed films on rigid substrates. I did a simple experiment at home by rolling up my sleeve (sweater): I saw a wavy pattern very similar to that shown in Fig. 3a, but it seems to me no ridge formation (Fig. 3e and 3i) occurred since I did not see anything as obvious as the ridge illustrated in Fig. 3e and 3i. I wonder if the pattern shown in Fig. 3a contains any ridges? Is it because ridges formed in reality usually have comparable amplitudes to wrinkles so that I did not recognize them?

2) We know that the effect of surface energy tends to be prominent in the micro-scale and nano-scale. For instability taking place at small length scales, like photo images shown in Fig. 4, does surface energy affect the instability pattern?

Hi Fan, Thanks for your reply and interest in our recent papers. Glad to know that you are covering this relatively new class of thin films. Though in atomic dimensions so that several new features appear, these films share a number of physical ingredients that select the inability patterns of bulk films. I look forward to your results on 2D material instabilities. We didn't post our raw data/images to make them public-accessible; If you are interested in or think they could help, feel free to contact my collaborators or me.

Hi Zhaohe, thanks for your comment. I noticed your excellent works on bending and tenting of 2D materials. In fact, our ongoing work shows that such dimensionless curvature effect also leads to intriguing responses in low-dimensional materials in nanoworld. I will share these results in the near furture and we may discuss later.

Hi Fan, Nice summary! I am trying to understand this interesting curvature effect. It is great to read this summary and then the references you organized. Thank you.